Property Hub

“In the real-world, we use modeling to project future property value.”

Driving Question: How can polynomial functions be used to make decisions about home values?

Standards:

AII.A-CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

AII.A-APR.B.2 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).

AII.A-APR.B.3 Identify zeros of polynomials when suitable factorizations are available and use the zeros to construct a rough graph of the function defined by the polynomial.

AII.F-IF.B.4?For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. *

AII.F-IF.B.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. *

AII.N-CN.C.9 (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials

AII.A-APR.D.6 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

This project has been designed to evaluate students’ ability to:

? Create a polynomial function in a real-life context

? Graph a polynomial function using technology

? Describe the features of a polynomial function

? Solve polynomial equations

? Evaluate polynomial models

? Use synthetic division to divide polynomials

Final product/ submission description:

In this project, you will be able to create a blog to promote and demonstrate to your audience the best home deals. You will include the mathematical data and other factors of your home deal. On the required date you will be submitting:

? Response Sheet

? blog

Due date: January 19, 2022

Criteria 4 3 2 1

Math Knowledge

(Response Sheet) 90% to 100% of mathematical concepts are completely understood. All terminology and notations are used appropriately. 80% to 90% of mathematical concepts are completely understood. Most terminology and notations are used appropriately. 70% to 80% of mathematical concepts are completely understood. Some terminology and notations are used. Fewer than 70% of mathematical concepts are understood. Terminology and notations are misused.

Math

Accuracy

(Response Sheet)

90% to 100% of the calculations are correct with all the work shown. 80% to 90% of the calculations are correct with all the work shown. 70% to 80% of the calculations are correct with some of the work shown. Fewer than 70% of the calculations are correct with no work shown.

Content

(Response Sheet)

95% to 100% of the facts are accurate, concise, current, and come mainly from reliable sources. 85% to 95% of the facts are accurate, concise, current, and come mainly from reliable sources. 75% to 85% of the facts are accurate, concise, current, and come mainly from reliable sources. Fewer than 75% of the facts are incomplete, out of date and/or incorrect. Information comes from no reliable source.

Independent work during class time

The student worked through the entire project without external help and consistently showed progress over time. The student worked through the project with little external help and consistently showed progress over time. The student worked through the project with some external help and inconsistently showed progress over time. The student could not work through the project independently and was unable to demonstrate progress over time.

Content

(Blog) Postings provide comprehensive insight, understanding, and reflective thought about the topic. Postings provide moderate insight, understanding and reflective thought about the topic. Postings provide minimal insight, understanding and reflective thought about the topic. Postings show no evidence of insight, understanding or reflective thought about the topic.

Layout

(Blog) Selects and inserts high quality graphics and multimedia when appropriate to enhance the content’s visual appeal and increase readability.

Selects and inserts graphics and multimedia that are mostly high quality and enhance and clarify the content.

Selects and inserts many low-quality graphics and multimedia which do not enhance the content.

Does not insert any graphics, or uses only low-quality graphics and multimedia, which do not enhance the content.

Reflection

(Response Sheet)

The reflection articulates

multiple connections

between this learning

experience and content from other courses, past

learning, life experiences and/or future goals. The reflection

articulates connections

between this learning

experience and content from other courses, past

learning experiences, and/or

future goals. The reflection attempts to articulate connections between this learning experience and content from other courses, past learning experiences, or personal goals, but the connection is vague or unclear. The reflection does

not articulate any

connection to other

learning or experiences.

Math Project Rubric

Property Hub

Part 1:

Suggested Resources:

Resource 1

Resource 2

a) Who is a real estate developer? What are the responsibilities of a real-estate developer? Elaborate in complete sentences using mathematical terms.

Real estate developer, or property developer, is a business process, encompassing activities that range from the renovation and re-lease of existing buildings to the purchase of raw land and the sale of developed land or parcels to others. Real estate developers are the people and companies who coordinate all of these activities, converting ideas from paper or mathematical equations to real property. Real estate development is different from construction or housebuilding, although many developers also manage the construction process or engage in housebuilding. Developers buy land, finance real estate deals, build or have builders build projects, develop projects in joint create, imagine, control, and orchestrate the process of development from the beginning to end. Developers usually take the greatest risk in the creation or renovation of real estate and receive the greatest rewards. Typically, developers purchase a tract of land, determine the marketing of the property, develop the building program and design, obtain the necessary public approval and financing, build the structures, and rent out, manage, and ultimately sell it.

b) As a real-estate developer, what questions do you ask your clients to make sure their needs are met? Write at least 4 questions in bullet form.

How long have you been looking for the property?

How much the person’s budget?

How many members are in your family?

Do you own now or are you renting?

Have you seen any homes or investment properties that you really liked?

How soon do you need to move?

If we can find the right property, are you prepared to make a decision now?

What price range have you been considering?

Are you going to pay cash or mortgage?

What are the dimensions of the property?

Part 2:

You are a real estate developer. You are exploring new markets to expand into and are researching the values of homes in different regions in USA.

USA is divided into 4 regions:

• Northeast

• Midwest

• South

• West

a) Use USA Data by Region to access the quarterly average sales price of houses sold by region. Choose 3 regions and the same quarter (first, second, third or last) then fill in the table below.

Note that:

? The first quarter corresponds to first of January

? The second quarter corresponds to first of April

? The third quarter corresponds to first of July

? The last quarter corresponds to first of October

Quarter___________________

Region

Year Average Home Sale Price Region

Year Average Home Sale Price Region

Year Average Home Sale Price

2010 2010 2010

2011 2011 2011

2012 2012 2012

2013 2013 2013

2014 2014 2014

2015 2015 2015

2016 2016 2016

2017 2017 2017

2018 2018 2018

2019 2019 2019

2020 2020 2020

b) Use Desmos calculator to sketch and write a polynomial function for each region/quarter that best fit the data. Your functions depend on the degree of the polynomial that you choose.

You may choose a cubic polynomial, a polynomial of degree 4 or a polynomial of degree 5. Use t=0 for the year 2010.

Region/Quarter Polynomial Function

c) Take a screenshot of each graph and paste it in the box below.

d) Does one of the regions/quarters appear to be the best fit? Explain your opinion in complete sentences using mathematical terms.

e) For each model, describe the end behavior and identify the maximum or minimum point(s).

Region 1:

Region 2:

c) Are there any turning points in any of the graphs? Justify your reasoning in complete sentences using mathematical terms.

d) Estimate the x- and y-intercept (s) of the graph of region 1. What do they mean in this context? Do those values make sense? Elaborate your answer in complete sentences.

e) Compare and contrast the end behavior of the 3 functions. What can you conclude? Write your answer in complete sentences.

f) Do you expect the home values in each region to be increasing or decreasing in the near future? Elaborate in complete sentences using mathematical terms.

Part 3:

It is important as a real estate developer that you can forecast the near future of real estate values.

a) Using your polynomial models, predict the future real estate values in each region/quarter you have chosen. Show your work.

Year Region 1 Region 2 Region 3

2024

2026

2028

2030

2040

b) When do you believe the models are most accurate? Use mathematical evidence to support your reasoning in complete sentences.

c) Which region is projected to have the highest home value in 2030?

d) Which region appears to be growing at the fastest rate? Use mathematical evidence to support your reasoning.

e) If the area of each house is represented by (x-5) square feet. Find approximately the area per square foot of the house in each region using synthetic division. Show your work.

Region 1:

Region 2:

Region 3:

Part 4:

Your real estate company typically sells homes around three different price points: $800,000, $1,000,000, $1,250,000.

a) Based on your models, find algebraically when the average home value in each region will aproximately reach these values. Show your work then fill in the table below.

Region 1:

Region 2:

Region 3:

Region 1 Region 2 Region 3

$800,000

$1,000,000

$1,250,000

b) Based on the results of your calculations, would your company be able to bring all three of your price points to any of the regions in USA before 2030? Use mathematical evidence to support your reasoning.

Part 5: Reflection

a) Other than region locations, what factors should you take into consideration when you plan to buy a new home? Write your answer in bullet form.

b) When you plan to buy a new home, how do you decide which home value is the best? Elaborate your answer in complete sentences using the math skills you have applied in your project.

c) List a minimum of four real-life applications of polynomial functions then explain one of them. Provide an example with solution of the application you have chosen. Write your answer in full sentences.

Part 6: Blog

As a real estate developer, you will display to your clients the top home asset through a blog. In the blog and based on mathematical data and other factors, you will promote the best deal among the three you have analyzed to meet the needs of your varying clients.

Steps to create a blog:

1. Use Simple Blog to start creating your blog.

2. Select Personal or Blog then select Blog.

3. Add a title to your blog then click “continue”. The title should be catchy and attractive.

4. Add a big, beautiful image or video at the top of your home page. Click on “I’ll upload my own” and select the image or video saved on your device, then click “add to website”.

5. Click “continue”, then fill in “the headline” by introducing yourself as a personal trainer and your blog, then click “add to website” Your blog's header is the first thing most visitors will notice, so it's important to make a good first impression.

6. Click “continue”, pick the layout you want for your Blog then click “continue” and pick a font style and a color palette, then click “continue”.

7. Choose a username for your blog then click “continue”.

8. Sign up with your email and password.

9. Once your website is created, click “add blog page”, then name your new blog page, then click “save page name”. The name should be simple, catchy, and related to the topic.

10. If an Ad pops up, click “not right now” then click “continue”.

11. Click “add content”, then “add text”. In the text, you should include:

? headline.

? the marketing plan for your best home deal. Display all factors that persuade your clients to buy a new home. Elaborate in complete sentences using mathematical terms and specific examples from the research you have done. Consider the wants and needs of your audience and whether they would find your blog posts convenient, informative, and enlightening.

12. Once you are done, click “share”, then “copy to clipboard” then paste the link in its designated place in the response sheet.

“In the real-world, we use modeling to project future property value.”

Driving Question: How can polynomial functions be used to make decisions about home values?

Standards:

AII.A-CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

AII.A-APR.B.2 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).

AII.A-APR.B.3 Identify zeros of polynomials when suitable factorizations are available and use the zeros to construct a rough graph of the function defined by the polynomial.

AII.F-IF.B.4?For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. *

AII.F-IF.B.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. *

AII.N-CN.C.9 (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials

AII.A-APR.D.6 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

This project has been designed to evaluate students’ ability to:

? Create a polynomial function in a real-life context

? Graph a polynomial function using technology

? Describe the features of a polynomial function

? Solve polynomial equations

? Evaluate polynomial models

? Use synthetic division to divide polynomials

Final product/ submission description:

In this project, you will be able to create a blog to promote and demonstrate to your audience the best home deals. You will include the mathematical data and other factors of your home deal. On the required date you will be submitting:

? Response Sheet

? blog

Due date: January 19, 2022

Criteria 4 3 2 1

Math Knowledge

(Response Sheet) 90% to 100% of mathematical concepts are completely understood. All terminology and notations are used appropriately. 80% to 90% of mathematical concepts are completely understood. Most terminology and notations are used appropriately. 70% to 80% of mathematical concepts are completely understood. Some terminology and notations are used. Fewer than 70% of mathematical concepts are understood. Terminology and notations are misused.

Math

Accuracy

(Response Sheet)

90% to 100% of the calculations are correct with all the work shown. 80% to 90% of the calculations are correct with all the work shown. 70% to 80% of the calculations are correct with some of the work shown. Fewer than 70% of the calculations are correct with no work shown.

Content

(Response Sheet)

95% to 100% of the facts are accurate, concise, current, and come mainly from reliable sources. 85% to 95% of the facts are accurate, concise, current, and come mainly from reliable sources. 75% to 85% of the facts are accurate, concise, current, and come mainly from reliable sources. Fewer than 75% of the facts are incomplete, out of date and/or incorrect. Information comes from no reliable source.

Independent work during class time

The student worked through the entire project without external help and consistently showed progress over time. The student worked through the project with little external help and consistently showed progress over time. The student worked through the project with some external help and inconsistently showed progress over time. The student could not work through the project independently and was unable to demonstrate progress over time.

Content

(Blog) Postings provide comprehensive insight, understanding, and reflective thought about the topic. Postings provide moderate insight, understanding and reflective thought about the topic. Postings provide minimal insight, understanding and reflective thought about the topic. Postings show no evidence of insight, understanding or reflective thought about the topic.

Layout

(Blog) Selects and inserts high quality graphics and multimedia when appropriate to enhance the content’s visual appeal and increase readability.

Selects and inserts graphics and multimedia that are mostly high quality and enhance and clarify the content.

Selects and inserts many low-quality graphics and multimedia which do not enhance the content.

Does not insert any graphics, or uses only low-quality graphics and multimedia, which do not enhance the content.

Reflection

(Response Sheet)

The reflection articulates

multiple connections

between this learning

experience and content from other courses, past

learning, life experiences and/or future goals. The reflection

articulates connections

between this learning

experience and content from other courses, past

learning experiences, and/or

future goals. The reflection attempts to articulate connections between this learning experience and content from other courses, past learning experiences, or personal goals, but the connection is vague or unclear. The reflection does

not articulate any

connection to other

learning or experiences.

Math Project Rubric

Property Hub

Part 1:

Suggested Resources:

Resource 1

Resource 2

a) Who is a real estate developer? What are the responsibilities of a real-estate developer? Elaborate in complete sentences using mathematical terms.

Real estate developer, or property developer, is a business process, encompassing activities that range from the renovation and re-lease of existing buildings to the purchase of raw land and the sale of developed land or parcels to others. Real estate developers are the people and companies who coordinate all of these activities, converting ideas from paper or mathematical equations to real property. Real estate development is different from construction or housebuilding, although many developers also manage the construction process or engage in housebuilding. Developers buy land, finance real estate deals, build or have builders build projects, develop projects in joint create, imagine, control, and orchestrate the process of development from the beginning to end. Developers usually take the greatest risk in the creation or renovation of real estate and receive the greatest rewards. Typically, developers purchase a tract of land, determine the marketing of the property, develop the building program and design, obtain the necessary public approval and financing, build the structures, and rent out, manage, and ultimately sell it.

b) As a real-estate developer, what questions do you ask your clients to make sure their needs are met? Write at least 4 questions in bullet form.

How long have you been looking for the property?

How much the person’s budget?

How many members are in your family?

Do you own now or are you renting?

Have you seen any homes or investment properties that you really liked?

How soon do you need to move?

If we can find the right property, are you prepared to make a decision now?

What price range have you been considering?

Are you going to pay cash or mortgage?

What are the dimensions of the property?

Part 2:

You are a real estate developer. You are exploring new markets to expand into and are researching the values of homes in different regions in USA.

USA is divided into 4 regions:

• Northeast

• Midwest

• South

• West

a) Use USA Data by Region to access the quarterly average sales price of houses sold by region. Choose 3 regions and the same quarter (first, second, third or last) then fill in the table below.

Note that:

? The first quarter corresponds to first of January

? The second quarter corresponds to first of April

? The third quarter corresponds to first of July

? The last quarter corresponds to first of October

Quarter___________________

Region

Year Average Home Sale Price Region

Year Average Home Sale Price Region

Year Average Home Sale Price

2010 2010 2010

2011 2011 2011

2012 2012 2012

2013 2013 2013

2014 2014 2014

2015 2015 2015

2016 2016 2016

2017 2017 2017

2018 2018 2018

2019 2019 2019

2020 2020 2020

b) Use Desmos calculator to sketch and write a polynomial function for each region/quarter that best fit the data. Your functions depend on the degree of the polynomial that you choose.

You may choose a cubic polynomial, a polynomial of degree 4 or a polynomial of degree 5. Use t=0 for the year 2010.

Region/Quarter Polynomial Function

c) Take a screenshot of each graph and paste it in the box below.

d) Does one of the regions/quarters appear to be the best fit? Explain your opinion in complete sentences using mathematical terms.

e) For each model, describe the end behavior and identify the maximum or minimum point(s).

Region 1:

Region 2:

c) Are there any turning points in any of the graphs? Justify your reasoning in complete sentences using mathematical terms.

d) Estimate the x- and y-intercept (s) of the graph of region 1. What do they mean in this context? Do those values make sense? Elaborate your answer in complete sentences.

e) Compare and contrast the end behavior of the 3 functions. What can you conclude? Write your answer in complete sentences.

f) Do you expect the home values in each region to be increasing or decreasing in the near future? Elaborate in complete sentences using mathematical terms.

Part 3:

It is important as a real estate developer that you can forecast the near future of real estate values.

a) Using your polynomial models, predict the future real estate values in each region/quarter you have chosen. Show your work.

Year Region 1 Region 2 Region 3

2024

2026

2028

2030

2040

b) When do you believe the models are most accurate? Use mathematical evidence to support your reasoning in complete sentences.

c) Which region is projected to have the highest home value in 2030?

d) Which region appears to be growing at the fastest rate? Use mathematical evidence to support your reasoning.

e) If the area of each house is represented by (x-5) square feet. Find approximately the area per square foot of the house in each region using synthetic division. Show your work.

Region 1:

Region 2:

Region 3:

Part 4:

Your real estate company typically sells homes around three different price points: $800,000, $1,000,000, $1,250,000.

a) Based on your models, find algebraically when the average home value in each region will aproximately reach these values. Show your work then fill in the table below.

Region 1:

Region 2:

Region 3:

Region 1 Region 2 Region 3

$800,000

$1,000,000

$1,250,000

b) Based on the results of your calculations, would your company be able to bring all three of your price points to any of the regions in USA before 2030? Use mathematical evidence to support your reasoning.

Part 5: Reflection

a) Other than region locations, what factors should you take into consideration when you plan to buy a new home? Write your answer in bullet form.

b) When you plan to buy a new home, how do you decide which home value is the best? Elaborate your answer in complete sentences using the math skills you have applied in your project.

c) List a minimum of four real-life applications of polynomial functions then explain one of them. Provide an example with solution of the application you have chosen. Write your answer in full sentences.

Part 6: Blog

As a real estate developer, you will display to your clients the top home asset through a blog. In the blog and based on mathematical data and other factors, you will promote the best deal among the three you have analyzed to meet the needs of your varying clients.

Steps to create a blog:

1. Use Simple Blog to start creating your blog.

2. Select Personal or Blog then select Blog.

3. Add a title to your blog then click “continue”. The title should be catchy and attractive.

4. Add a big, beautiful image or video at the top of your home page. Click on “I’ll upload my own” and select the image or video saved on your device, then click “add to website”.

5. Click “continue”, then fill in “the headline” by introducing yourself as a personal trainer and your blog, then click “add to website” Your blog's header is the first thing most visitors will notice, so it's important to make a good first impression.

6. Click “continue”, pick the layout you want for your Blog then click “continue” and pick a font style and a color palette, then click “continue”.

7. Choose a username for your blog then click “continue”.

8. Sign up with your email and password.

9. Once your website is created, click “add blog page”, then name your new blog page, then click “save page name”. The name should be simple, catchy, and related to the topic.

10. If an Ad pops up, click “not right now” then click “continue”.

11. Click “add content”, then “add text”. In the text, you should include:

? headline.

? the marketing plan for your best home deal. Display all factors that persuade your clients to buy a new home. Elaborate in complete sentences using mathematical terms and specific examples from the research you have done. Consider the wants and needs of your audience and whether they would find your blog posts convenient, informative, and enlightening.

12. Once you are done, click “share”, then “copy to clipboard” then paste the link in its designated place in the response sheet.

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